Complexity and Learning

Math equations written on a blackboard - mathematics and science concepts

 

Learning is to cognition what evolution is to life. According to the prescient thinker, scientist and innovator, Ray Kurzweil, Evolution happens by indirection, - each stage or epoch becomes the starting point for the next stage or epoch. Likewise, learning also happens by indirection. Each level of learning becomes the starting point for the next level of learning. In this, learning resembles wavefront propagation. In physics, wavefront propagation is governed by the Huygens principle. Each point on a given wavefront becomes the starting point for the generation of the next wavefront. How does this analogy help clarify the process of learning by indirection? To see this it is helpful to consider that the Huygens principle to work requires an odd number of spatial dimensions. In an even number of spatial dimensions, the wave equation degenerates into a diffusion or heat equation. Likewise, learning to maintain its growth by indirection requires certain conditions placed on the environment. These conditions determine whether learning begins or arises from a given level. Here's where complexity enters into the process.

Leonardo & Da Vinci

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